I've got to say, it's with a great reluctance that I will condone the labelling of the Covenant cruiser on "Keyes" as also the Truth and Reconciliation. For one, Cortana is just too ambiguous ("The Flood overwhelmed this cruiser..."). And another thing...

ÓSure, we stopped the Covenant from making off with any good bits of the ring, cut short the Flood's galactic joyride in the Truth and Reconciliation and knocked the gun pointed at the head of the universe out of the Monitor's hands, but the people of Earth still watch the sky every night, waiting for the hammer to fall.Ž

Tada! An official statement by Jason Jones confirms the identity of the ship in the level Keyes! Now I will answer Hedgemonyžs concerns:

Cortana probably says that the Flood disabled the ship because it was probably fixed by the time that the Flood had got to it. Besides, if it were out in space, how could the Flood attack it without having a large, powerful ship of their own? It seems to me that the Truth and Reconciliation had been repaired and was ready for departure, but was then disabled by the Flood.

Cortana was correct when she said that a shuttle bay should be ÓhereŽ?after saying Óhere,Ž she places a way-point, which you follow to a shuttle bay. Her records are accurate, because they are the records for the Truth and Reconciliation, which is the same ship in both levels.